In most of the multi–criteria decision–analysis (MCDA) problems in which the Choquet integral is used as aggregation function, the coefficients of Choquet integral (capacity) are not known in advance. Actually, they could be calculated by capacity definition methods. In these methods, the preference information of decision maker (DM) is used to constitute a possible solution space. ...

In works dealing with capacities (fuzzy measures) and the Choquet integral on finite spaces, it is usually considered that all subsets of the universe are measureable. Hence, all functions are integrable in the sense of Choquet. We consider the situation where some subsets are not measurable (not feasible), so that there are nonintegrable functions. Since this is a severe limitation in applicat...

A Sugeno and a Choquet integrals are commonly used fuzzy integrals for aggregation. As a generalization of both integrals, the twofold integral is induced. The twofold integral enables us to interpret two measures from a different semantics viewpoint. One corresponds to the Choquet integral and the other corresponds to the Sugeno integral. Our work is about building models for the twofold integ...

Financial distress prediction (FDP) has always been an important issue in the business and financial management. This research proposed a novel multiple classifier ensemble model based on firm life cycle and Choquet integral for FDP, named MCELCCh-FDP, as a new approach to tackle with financial distress. Empirical study based on Chinese listed companies’ real data is conducted, and the results ...

Jang, Kim and Kwon introduced a multi-valued Choquet integral for multifunctions with respect to real fuzzy measures and Zhang, Guo and Liu established for this kind of integral some convergence theorems. The aim of this paper is to present another type of set-valued Choquet integral, called by us the Aumann-Choquet integral, for non-negative measurable functions with respect to multisubmeasure...

The usefulness of the Choquet integral for modelling decision under risk and uncertainty is shown. It is shown that some paradoxes of expected utility theory are solved using Choquet integral. It is shown that Choquet expected utility model for decision under uncertainty and rank dependent utility model for decision under risk are respectively same as their simplified version.

This paper presents an ordered sorting procedure based on the Choquet integral as a discriminant function. It uses information provided by the Decision Maker (dm) in terms of a set of prototypes (alternatives well-known to the dm). The capacities of the Choquet integral are assessed through the solving of a linear program or a quadratic program. An interpretation of the results is provided by m...

In the context of multicriteria decision making whose aggregation process is based on the Choquet integral, bi-capacities can be regarded as a natural extension of capacities when the underlying evaluation scale is bipolar. The notion of entropy, recently generalized to capacities to measure their uniformity, is now extended to bi-capacities. We show that the resulting entropy measure has a ver...

Based on the concept of an interval-valued function which is motivated by the goal to represent an uncertain function, we define the Choquet integral with respect to a fuzzy measure of intervalvalued functions. We also discuss convergence in the C mean and convergence in a fuzzy measure of sequences of measurable interval-valued functions. In particular, we investigate the convergence theorem f...

Résumé : L’utilisation de l’intégrale de Choquet en Aide Multicritère à la Décision (AMCD) nécessite l’identification de la capacité qui lui est associée. Nous proposons ici un algorithme de détermination d’une capacité pour l’intégrale de Choquet 2-additive à partir d’une information ordinale fournie par le décideur. Mots-clés : AMCD, intégrale de Choquet, capacité 2-additive. Abstract: The us...